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Quantifying the relationship between pollinator behavior and plant reproductive isolation
Robin Hopkins
The Department of Organismic and Evolutionary Biology and
The Arnold Arboretum
Harvard University
1300 Centre St
Boston, MA 02131
[email protected]
1
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ABSTRACT
Pollinator behavior is an important contributor to reproductive isolation in plants. Despite
hundreds of years of empirical research, we lack a quantitative framework for evaluating how
variation in pollinator behavior causes variation in reproductive isolation in plants. Here I present
a model describing how two aspects of pollinator behavior – constancy and preference – lead to
reproductive isolation in plants. This model is motivated by two empirical observations: most cooccurring plants vary in frequency over space and time and most plants have multiple pollinators
that differ in behavior. These two observations suggest a need to understand how plant frequency
and pollinator frequency influence reproductive isolation between co-occurring plants. My
model predicts how the proportion of heterospecific matings varies over plant frequencies given
pollinator preference and constancy. I find that the shape of this relationship is dependent on the
strength of pollinator behavior. Additionally, my model incorporates multiple pollinators with
different behaviors to predict the proportion of heterospecific matings across pollinator
frequencies. I find that when two pollinators display different strength constancy the total
proportion of heterospecific matings is simply the average proportion of heterospecific matings
predicted for each pollinator. When pollinators vary in their preference the pollinator with the
stronger preference disproportionally contributes to the predicted proportion of total
heterospecific matings. I apply this model to examples of pollinator-mediated reproductive
isolation in Phlox and in Mimulus to predict relationships between plant and pollinator frequency
and reproductive isolation in natural systems.
2
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INTRODUCTION
The notion that pollinator behavior is important for plant diversification and speciation
can be traced to Darwin’s foundational ideas of evolution by natural selection (Darwin 1862).
For many angiosperms, animals are necessary vectors for pollen movement between outcrossing
individuals (Ollerton et al. 2011). It has long been argued that plants have evolved elaborate
floral traits, including variable size, color, shape, and scent to attract and influence the behavior
of pollinators (Campbell et al. 1997; Galen 1989; Schemske and Bradshaw 1999; Stanton et al.
1986). Furthermore, there is phylogenetic evidence that diversification in angiosperms is driven,
in part, by pollinators (Valente et al. 2012; Van der Niet and Johnson 2012; Whittall and Hodges
2007). From a plant’s perspective, pollinator visits are only fruitful if the pollinator moves pollen
between conspecific plants. Heterospecific pollen movement can result in hybridization, wasted
pollen and, in some cases, stigma clogging (Morales and Traveset 2008). Because of the intimate
tie between pollinator behavior and reproduction, ethological isolation can be an important
barrier to heterospecific mating (reviewed in Grant 1949; Kay and Sargent 2009; Van Der Niet et
al. 2014). Despite numerous studies documenting pollinator mediated reproductive isolation in
plants, we still lack a quantitative framework linking variation in pollinator behavior to variation
in heterospecific pollen movement.
Pollinators impose strong selection on floral traits and it is thought that plants evolve to
best utilize the most effective pollinator (reviewed in Fenster et al. 2004; Harder and Johnson
2009; Rosas-Guerrero et al. 2014; Schiestl and Johnson 2013). Pollinators can in turn cause
reproductive isolation between closely related taxa. A number of case studies demonstrate the
importance of pollinator behavior in causing reproductive isolation between sympatric species
(e.g. Hopkins and Rausher 2012; Kay and Schemske 2003; Klahre et al. 2011; Ramsey et al.
3
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2003), and reviews of reproductive isolation in plants more generally have found that pollinator
mediated reproductive isolation has significantly contributed to speciation in plants (Baack et al.
2015; Lowry et al. 2008). Yet, there is still doubt as to the effectiveness of pollinators in
preventing heterospecfic gene flow (Chittka et al. 1999; Waser 1998). Most plants are generalists
appealing to a variety of pollinators, and most pollinators are generalists visiting a variety of
plants (Jordano 1987; Ollerton 2016; Robertson 1928; Waser et al. 1996). How then can
pollinators cause reproductive isolation? In order to better address this question we need a
framework for evaluating how quantifiable properties of pollinator behavior lead to reproductive
isolation in plants.
Two aspects of pollinator behavior – preference and constancy – influence reproductive
isolation in plants. The relative importance of constancy and preference to plant reproductive
isolation has been debated in the literature (Kay and Sargent 2009; Waser 1998) but a direct
comparison has never been possible. There is currently no method for comparing the strength of
preference to the strength of constancy and determining their respective contributions to
heterospecific pollen movement.
Pollinator preference is the tendency of a pollinator to visit one species or variety of plant
more than is expected based on that plant’s frequency in a population. Preference can be
expressed in response to an assortment of traits, such as color, size, shape, and smell, which
often act as signals for a reward such as nectar (Schiestl and Johnson 2013). Increased pollinator
visitation due to preference is an important agent of selection implicated in the evolution and
divergence of floral traits (e.g. Alexandersson and Johnson 2002; Benitez-Vieyra et al. 2006;
Campbell et al. 1996; Mitchell et al. 1998). Preference can also cause reproductive isolation (e.g.
Bradshaw and Schemske 2003; Fulton and Hodges 1999; Hoballah et al. 2007; Martin et al.
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2008). In a community with two plant species, a pollinator that strongly prefers one species will
have less opportunity to move pollen between species of plants than a pollinator that visits both
species equally. For example, hummingbirds strongly prefer the red flowers of Mimulus
cardinalis while bees prefer the pink flowers of Mimulus lewisii (Bradshaw and Schemske
2003). This pollinator specialization results in hummingbirds transferring pollen between M.
cardinalis individuals, bees transfering pollen between M. lewisii individuals, and few
heterospecific pollen transfers.
Pollinator constancy is the tendency of pollinators to move between the same species or
variety of plant more than between different plants given what is expected based on the
proportion of each plant visited (Waser 1986). Constancy describes the order of visits to plants
rather than the number of visits to each type of plant. For example, in the Texas Phlox
wildflower system, dark-red P. drummondii plants co-occur with the light-blue P. cuspidata
plants and the two species share pollinators (Hopkins and Rausher 2012). Despite visiting both
species of Phlox, the butterfly pollinators tend to move between plants of the same species more
than plants of different species (Hopkins and Rausher 2012). In other words they go from a darkred, to a dark-red, to a dark-red flower and then switch to go from a light-blue, to a light-blue, to
a light-blue flower. In this way constancy causes reproductive isolation because pollen is
transferred between conspecific individuals more than between heterospecific individuals.
Foraging with constancy has been studied most in honeybees and bumblebees (Gegear and
Laverty 2005; Hill et al. 1997; Kephart and Theiss 2004; Marques et al. 2007; Raine and Chittka
2005) but has been documented in Lepidoptera (Aldridge and Campbell 2007; Goulson and Cory
1993; Goulson et al. 1997; Hopkins and Rausher 2012; Kulkarni 1999; Lewis 1986) and
hoverflies as well (Goulson and Wright 1998). Although, it is still unclear why pollinators forage
5
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with constancy, it has been hypothesized that it is an adaptive foraging strategy that optimizes
efficiency of resource acquisition (Gegear and Thomson 2004; Goulson 1999).
Co-occurring plant species vary extensively in relative frequency over space and time.
Intuitively, the proportion of heterospecific pollen transfers is correlated with the relative
frequency of plant species. If a population is predominately made up of one species, just by
chance there will be fewer opportunities for a pollinator to transfer pollen from the rare species
to the common species than between the common species. But, we lack an understanding of how
aspects of pollinator behavior, such as constancy and preference, affect this relationship between
heterospecific pollen transfer and plant frequency.
Most plants are visited by multiple pollinators (Robertson 1928; Waser et al. 1996) that
do not show the same behavioral responses to floral signals. How is reproductive isolation in
plants affected if one pollinator has strong preference and another has weak preference? What if
the frequency of these two pollinators varies across populations? A quantitative framework for
understanding how multiple pollinators that express different behavior interact to cause
reproductive isolation in plants is needed.
To address these gaps in our knowledge of pollinator mediated reproductive isolation I
construct a mathematical model that describes how aspects of pollinator behavior cause
heterospecific matings in plants. My specific goals are: 1.) To define a mathematical relationship
between pollinator behavior (constancy and preference) and plant reproductive isolation, 2.) To
determine how variation in plant frequency affects plant reproductive isolation and 3.) To
determine how variation in pollinator frequency affects plant hybridization in a community with
multiple pollinators. To demonstrate the relevance of this work to empirical investigations of
plant-pollinator interactions, I apply this model to natural examples to predict proportion of
6
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heterospecific matings given preference and constancy measures taken from field trials with
sympatric plants.
MODEL
I present a deterministic model that describes how pollinator behavior leads to movement
of pollen between conspecific and heterospecific plants. The notation used in my model is
defined in Table 1. The goal of the model is to predict the proportion of heterospecific matings
(H) between two co-occurring plant taxa, given pollinator behavior. This is a simplified model
based on two parameters describing aspects of pollinator behavior – preference and constancy.
The model investigates how the proportion of heterospecific matings varies with frequency of a
pollinator and frequency of a plant. For simplicity I will start by describing a system with a
single pollinator and two plants in which one plant is the focal species and the other is the
heterospecific pollen donor. I will go on to describe a system with two pollinators and two plant
species. Online Appendix A describes a generalized model that allows for unlimited plants and
pollinators.
Table 1. Summary of notation and definitions for model
Notation
H
ρ
κ
f
ψ
𝑣
𝜙
Description
Proportion of heterospecific pollen transfers (matings)
Pollinator Preference
Pollinator constancy
Focal plant frequency
Proportion of visits a pollinator makes to a focal plant
Proportion of focal plant’s total visits made by a pollinator
Proportion of total visits (across all plants in the community) made by a
pollinator
One pollinator model
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For a given pollinator the proportion of visits (ψ) to a focal plant can be described as a
function of its preference (ρ) for the plant and the plant frequency (f).
!"
𝜓 = !"!(!!!)
(1)
Equation 1 is modified from a foraging preference function in Greenwood and Elton (1979) as in
Smithson and Macnair (1996) and can be adapted to include frequency dependent variation in
preference (Online Appendix B). The proportion of visits to a plant species varies between 0 and
1 and increases as both frequency of the plant increases and preference for the plant increases.
Preference varies from 0 to infinity and determines how much a pollinator over or under visits a
plant given its frequency. If a pollinator shows no preference ρ = 1 and proportion of visits is
equal to the frequency of the focal plant. If ρ > 1 a pollinator favors the focal species by visiting
it ρ times more than is expected based on the plant frequency. In other words, if ρ = 2 a
pollinator visits the focal species twice as much as the other plant given their frequencies. When
ρ < 1 a pollinator disfavors the focal species and will visit it proportionally less. Preference for a
given plant type is always relative to at least one other plant type in the population.
Pollinator constancy (κ) is a measure of the conspecific versus heterospecific transitions a
pollinator makes given what is expected based on the frequency of visits to each plant.
Constancy varies between -1 and 1, with negative constancy indicating more heterospecific
transitions than expected and positive constancy indicating more conspecific transitions than
expected. When observing pollinator movement, constancy can be calculated based on the
observed proportion of heterospecific transfers (H) made by a pollinator to a plant and the
observed proportion of visits to the focal species by the pollinator (ψ).
𝜅=
!!! !!
!!! !!!!!(!!!)
8
(2)
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Equation 2 is modified from the constancy formula presented in Gegear and Thomson (2004).
This equation can be solved for H in terms of constancy and proportion of visits. This yields
𝐻=
(!!!)(!!!)
!!!!!!"
(3a)
where the proportion of heterospecific pollen transfers is a function of preference and frequency
of the focal plant. This can then be expanded to create an equation describing the proportion of
heterospecific matings in terms of preference, constancy, and frequency of plants.
!!! (!!!)
𝐻 = !!!!!(!!!!!!!!")
(3b)
Equation 3b predicts the proportion of heterospecific pollen transfers a plant will experience
given the preference and constancy of a pollinator.
The effect of preference
The proportion of heterospecific matings has an inverse relationship with focal plant
frequency. The shape of this relationship depends on the strength of pollinator preference. With
no constancy (i.e. expected number of conspecific transitions given frequency of visits),
!!!
𝐻 = !!!"!! , κ = 0
(4)
where the proportion of heterospecific matings is a function of pollinator preference and
frequency of the focal plant. Figure 1a shows equation 4 evaluated for no preference, strong
preference, weak preference, and preference against a focal plant.
The way in which plant frequency affects heterospecific matings depends on the strength
of pollinator preference in the system. With no preference, 𝐻 = 1 − 𝑓 , such that the proportion
of heterospecific matings is the inverse of the focal plant frequency. When a pollinator has
preference for the focal species heterospecfic mating is a convex function of frequency. When a
9
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pollinator has preference against the focal species heterospecific mating becomes a concave
function of frequency. The curvature of the function is determined by the strength of preference.
When preference is strong (𝜌 = 10) and the focal plant is rare, small changes in plant frequency
can result in significant declines in heterospecfic matings. When preference is weak (𝜌 = 2), the
proportion of heterospecfic matings decreases less with an equivalent change in plant frequency.
With strong preference against the focal species (𝜌 = 0.1), heterospecific matings remain
frequent even at high focal plant frequencies and drop off precipitously as the focal plant
1.0
C.
Constancy
ρ=10, κ=0.8
ρ=2, κ=0.8
ρ=10, κ=0.3
ρ=2, κ=0.3
0.4
0.6
Plant Frequency (f )
0.8
1.0
0.8
0.6
0.4
Proportion of heterospecific matings (H)
0.0
0.0
0.2
0.2
0.8
0.6
0.4
Proportion of heterospecific matings (H)
0.8
0.6
0.4
0.2
0.0
Preference and Constancy
κ=0.8
κ=0.3
κ=0
κ=-0.8
0.2
1.0
B.
Preference
ρ=10
ρ=2
ρ=1
ρ=0.1
0.0
Proportion of heterospecific matings (H)
A.
1.0
becomes fixed in the population.
0.0
0.2
0.4
0.6
Plant Frequency (f )
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Plant Frequency (f )
Figure 1: The relationship between plant frequency and proportion of heterospecific matings when pollinators
have different preference and constancy. In A., examples of pollinators with no constancy (κ = 0) and strong
preference for a plant (ρ =10, black line), weak preference for a plant (ρ=2, gray line), no preference for plant
(ρ=1, dotted line), and strong preference against a plant (ρ=0.1, dashed line) show how the heterospecfic mating
function is convex, linear, or concave depending on the strength and direction of preference. In B., examples of
pollinators with no preference (ρ = 1) and strong constancy (κ = 0.8, black solid line), weak constancy (κ = 0.3,
gray line), no constancy (κ = 0, dotted line), and negative constancy (κ =-0.8, dashed line) show how the
heterospecific mating function depends on the strength of constancy. In C., examples of pollinators with strong
preference and strong constancy (solid black line), weak preference and strong constancy (dashed black line);
strong preference and weak constancy (solid gray line), and weak preference and weak constancy (dashed gray
line) demonstrate how the affect of constancy and preference on heterospecific matings interact and can be
compared.
The effect of constancy
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Similar to preference, a change in pollinator constancy will affect the way plant
heterospecfic matings vary with plant frequency. In a system with no pollinator preference (ρ =
1),
𝐻=
(!!!)(!!!)
!! !!!! !
,ρ=1
(5)
the proportion of heterospecific matings becomes a function of plant frequency and constancy.
Figure 1b shows equation 5 evaluated for strong constancy, weak constancy, and strong negative
constancy. Constancy causes heterospecific mating to be a convex function of plant frequency
and negative constancy causes heterospecfic mating to be a concave function of plant frequency.
The curvature of this function is dependent on the strength of constancy.
Equation 3b can be used to compare the relative importance of preference and constancy
for plant reproductive isolation and how the two aspects of pollinator behavior interact. For
example, Figure 1c shows how strong and weak preference and constancy interact. For these
parameter values, a pollinator with strong preference and weak constancy is similar to a
pollinator with strong constancy and weak preference.
Two pollinator model
Most plants receive visits from multiple pollinators that display different behavioral
responses to floral traits. This observation motivates the need to understand how multiple
pollinators with different strength preference and constancy combine to cause the total
proportion of heterospecific matings a plant experiences. As mentioned above, I describe a
model with two pollinators here and generalize this for any number of pollinators in Online
Appendix A.
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The total proportion of heterospecific pollen transferred to a plant is determined by the
heterospecific pollen transferred by each pollinator proportional to the pollinator visitation rates.
For a two pollinator system
𝐻 = 𝜐! 𝐻! + (1 − 𝜐! )𝐻!
(6)
where 𝐻 is the total proportion of heterospecific matings for a focal plant. In this equation, 𝐻!
and 𝐻! are the proportion of heterospecific pollen transfers from pollinator 1 and pollinator 2
respectively, and 𝑣! is the proportion of a plant’s total visits made by pollinator 1. I can define 𝑣!
as
𝑣! = !
!! !!
! !! !(!!!! )!!
(7)
where 𝜙! is the frequency of visits by pollinator 1 across all plants. This term is related but
distinct from pollinator frequency in a community because different types of pollinators may
have different absolute numbers of visits. For the purpose of this model I am interested in
frequency of visits across all plants. Additionally, this is distinct from 𝜓! and 𝜓! , which are the
proportion of visits pollinator 1 and 2 make to the focal plant. As above, 𝜓! and 𝜓! are functions
of pollinator preference and plant frequency (equation 1). In this way the total proportion of
heterospecific matings for a focal species can be predicted from pollinator behavior (preference
and constancy), plant frequency, and pollinator visit frequency.
𝐻=
(!!!)(
!! ! !! !! !!! !! !!
! (!!!) !! !! !!! !! !!
! !
!!!! !! (!!!!! !!! !!! !! ) !!!! !! (!!!!! !!! !!! !! )
!!! ! !!! !!! (!!!!! !! !!!! )
(8)
To explore the behavior of this equation I investigate variation in pollinator constancy and
preference separately. For each aspect of behavior I show how the proportion of heterospecific
matings varies across focal plant frequency when pollinator frequency is held at 50%, and across
pollinator frequency when focal plant frequency is held at 50%.
12
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Effect of preference across plant and pollinator frequency
First, I explore the way in which multiple pollinators that differ in preference affect the
proportion of heterospecfic matings. If plant frequency is held at 50%, the proportion of
heterospecfic matings is a nonlinear function of pollinator frequency (Figure 2a). This concave
relationship reveals that the predicted proportion of heterospecific matings from two pollinators
with different preference is not simply the average of the heterospecific matings by each
pollinator, as this would predict a straight line. Instead, the pollinator with stronger preference
for the focal plant disproportionally influences the total proportion of heterospecific matings.
0.0
0.2
0.4
0.6
0.8
1.0
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
Preference
ρ1=10, ρ2=1
ρ1=10, ρ2=0.1
ρ1=1, ρ2=1
ρ1=2, ρ2=0.1
ρ1=2, ρ2=0.5
Proportion of heterospecific matings (H)
1.0
B.
0.0
Proportion of heterospecific matings (H)
A.
0.0
Pollinator Visit Frequency (φ)
0.2
0.4
0.6
0.8
1.0
Plant Frequency (f )
Figure 2: The relationship between plant frequency and proportion of heterospecific matings when two
pollinators differ in preference across pollinator frequency (A.), or plant frequency (B.). Both plots show
examples of pollinators with no constancy (κ = 0), but different strengths of preference. Black lines are scenarios
with one pollinator having strong preference (ρ1 =10), and gray lines are when one pollinator has weak
preference (ρ1=2) or no preference (ρ1= 1, dotted). Solid lines show when a second pollinator has no preference
(ρ2 = 1, black) or weak preference against (ρ2 = 0.5, gray) and dashed lines show when a second pollinator has
strong preference against the focal plant (ρ2=0.1). Note how dashed lines fall below solid lines across most
pollinator frequencies.
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The magnitude of this deviation from the linear average is proportional to the difference in
preference between the two pollinators. This means that a plant receives fewer heterospecific
matings when it has one pollinator that has strong preference against it, than if it has one
pollinator with no preference at all (i.e. the black dashed line is below the black solid line) across
most pollinator frequencies.
Second, I demonstrate the relationship between plant frequency and heterospecific
matings when two pollinators are at equal frequency but differ in their preference (Figure 2b). I
show a scenario for which one pollinator has strong preference and one pollinator has no
preference for the focal plant (solid black line). This reveals a non-linear relationship between
plant frequency and heterospecific matings such that at low focal-plant frequencies, small
changes in plant frequency result in large decreases in heterospecfic matings. This rate of change
in heterospecfic matings decreases as plant frequency increases. When one pollinator has strong
preference for the focal plant and one pollinator that has strong preference against the focal plant
(black dashed line), heterospecific mating becomes a non-monotonic function of plant frequency.
Under some conditions heterospecific mating can actually increase as focal plant frequency
increases. Although, across most plant frequencies (i.e. 0.3< f <0.9) the proportion of
heterospecific matings changes very little. Of note, across many plant frequencies (i.e 0< f <0.67
in figure 2b) a focal plant has less heterospecfic matings when one pollinator has strong
preference against the focal plant than if one pollinator has no preference at all. In Figure 2b this
occurs when the dashed black and gray lines are below the solid black and gray lines.
Effect of constancy across plant and pollinator frequency
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I explore the relationship between plant frequency and proportion of heterospecific
matings when a plant has two pollinators that differ in the strength of constancy. If pollinators
show no preference, (𝜌 = 1), then 𝑣! , the proportion of a plant’s total visits made by pollinator 1,
equals the proportion of total visits pollinator 1 makes in the system (𝜙! ). Therefore, the total
proportion of heterospecific matings for a plant is the average of the proportion of heterospecific
matings made by each butterfly weighted by the frequency of the butterfly in the system. Thus,
in a two-pollinator system, the proportion of heterospecific matings varies linearly with
pollinator frequency (Figure 3a). The slope of this line is determined by the difference in the
proportion of heterospecific matings predicted by the two pollinators. Equation 6 can be
rearranged to describe the linear relationship between total heterospecific matings and proportion
0.0
0.2
0.4
0.6
0.8
1.0
1.0
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
κ1=0.8, κ2=0
κ1=0.8, κ2=-0.8
κ1=0, κ2=0
κ1=0.3, κ2=-0.8
κ1=0.3, κ2=-0.3
0.0
Constancy
Proportion of heterospecific matings (H)
1.0
B.
0.0
Proportion of heterospecific matings (H)
A.
0.0
Pollinator Visit Frequency (φ)
0.2
0.4
0.6
0.8
1.0
Plant Frequency (f )
Figure 3: The relationship between plant frequency and proportion of heterospecific matings when two
pollinators differ in constancy across pollinator frequency (A.), or plant frequency (B.). Both plots show
examples of pollinators with no preference (ρ = 1), but different strengths of constancy. Black lines are scenarios
with one pollinator having strong constancy (κ1 =0.8), and gray lines are when one pollinator has weak
constancy (κ1=0.3) or no constancy (κ1= 0, dotted). Solid lines show when a second pollinator has no constancy
(κ2 = 0, black) or weak negative constancy (κ2 = -0.3, gray) and dashed line shows when a second pollinator has
strong negative constancy (κ2=-0.8).
15
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of visits in the system by a pollinator:
𝐻 = (𝐻! − 𝐻! )𝜙 + 𝐻!
(9)
In figure 3b, I show the relationship between pollinator frequency and proportion of
heterospecific matings when two pollinators differ in the strength of constancy. In a twopollinator system, the total proportion of heterospecific matings is the average of the proportions
predicted by each pollinator independently. Recall that the relationship between heterospecfic
matings and plant frequency is non-linear in a one-pollinator system therefore it is also nonlinear in a two-pollinator system. Note, unlike with preference variation, a plant always has
fewer heterospecific matings when one of its pollinators has no constancy than when a pollinator
has negative constancy.
Model applications
Below I apply this mathematical model to empirical data of pollinator behavior. Details
of how to identify and calculate the necessary parameters from field observations are described
in Online Appendix C.
Pollinator preference and constancy for Phlox
Previous work shows that pollinator behavior is a significant reproductive isolating
barrier between sympatric P. drummondii and P. cuspidata (Hopkins et al. 2014). Flower color
divergence in P. drummondii is due to reinforcement. A change in flower color evolved in
sympatric populations because the derived color decreased heterospecific matings between these
two Phlox species (Hopkins et al. 2014). Specifically, when both Phlox had the ancestral lightblue flower color the pollinator Battus philinor (the Pipevine Swallowtail) moved pollen
extensively between the two species, but when P. drummondii had dark-red flower color, the
butterfly made significantly fewer transitions between species and more transitions within
16
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pollinator observations were done on
arrays of plants at fixed frequency (60%
0.8
Phlox Parameters
Dark-Red, ρ=5.4, κ=0.36
Light-blue, ρ=4.8, κ=-0.35
0.6
P. cuspidata, 20% dark-red P.
drummondii, and 20% light-blue P.
0.4
drummondii). The observations indicate
that the change in flower color can
0.2
Proportion of matings with Phlox cuspidata
1.0
species (Hopkins et al. 2014). These
0.0
decrease heterospecific matings by 50%,
0.0
0.2
0.4
0.6
0.8
1.0
Phlox drummondii Frequency
but how do the proportion of
heterospecific matings for light-blue and
Figure 4: Predicted proportion of heterospecific matings
between Phlox drummondii and Phlox cuspidata across P.
drummondii frequency. Preference and constancy were
estimated from field observations described by Hopkins et al
(2014). Equation 3b was used to evaluate proportion of
heterospecific matings.
dark-red plants vary across different
frequencies of Phlox as you might
expect to find in the wild? I use equation
3b to evaluate the expected proportion of heterospecific matings for light-blue and dark-red P.
drummondii across plant frequencies given B. philenor behavior (Figure 4). Based on the field
observations of B. philenor, I used equation 1 and equation 2 to calculate preference and
constancy, respectively. Across all P. drummondii frequencies, dark-red flowers are expected to
have a lower proportion of heterospecific matings than light-blue flowers. As noted previously,
this difference in predicted heterospecific matings is due to variation in pollinator constancy
based on flower color. The expected difference between the two colors decreases at both high
and low frequencies. Since the strength of reinforcing selection is proportional to the difference
in heterospecific matings between the two flower colors, these results suggest that the strength of
reinforcing selection is dependent on the frequency of the two species of plants in the population.
17
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Two pollinators’ preferences for Mimulus
A classically studied species pair for which pollinator behavior is known to play an
important role in reproductive isolation is Mimulus cardinalis and Mimulus lewisii (Ramsey et al.
2003). These two species differ in a number of floral traits that influence pollinator preference
such that hummingbirds strongly prefer M. cardinalis and bees strongly prefer M. lewisii
(Bradshaw and Schemske 2003; Byers et al. 2014; Ramsey et al. 2003; Schemske and Bradshaw
1999). Based on the pollinator observation data reported by Ramsey et al. (2003) on natural
populations of the two Mimulus species, I
0.8
Mimulus Parameters
M. cardinalis, bird ρ=78.6, bee ρ=0.0035
M. lewisii, bird ρ=0.013, bee ρ=284.7
number of visits to each species by each
pollinator and the frequency of each plant
0.6
species. These two species grow across an
0.4
elevation cline with M. cardinalis tending
0.2
to grow more at lower elevations and M.
lewisii found at higher elevation (Ramsey
et al. 2003). Across this cline there is
0.0
Proportion of matings with heterospecific Mimulus
1.0
quantified pollinator preference from the
0.0
0.2
0.4
0.6
0.8
1.0
Mimulus cardinalis Frequency
Figure 5: Predicted proportion of heterospecific matings
between M. cardinalis and M. lewisii. Preference for both
hummingbirds (bird) and bees were estimated from field
observations described by Ramsey et al (2003). Equation 8
was used to evaluate proportion of heterospecific matings.
presumably variation in the relative
frequency of the two species. I evaluate
how heterospecifc matings between these
two species is predicted to change across
plant frequency given the pollinator preference observed in the field. Figure 4 shows equation 8
evaluated across frequencies of M. cardinalis for both species of Mimulus. As expected given the
18
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strong preference observed, reproductive isolation is nearly complete for both M. cardinalis
(solid line) and M. lewisii (dashed line). The simplest form of my model, assuming no frequency
dependent change in preference, predicts a higher proportion of heterospecific matings at the
edges of the cline when one of the two species is rare. Intuitively, one might expect the highest
rate of hybridization to be when both species are coexisting at equal frequency. In fact this is
exactly the opposite of what my model predicts. At high frequencies, M. cardinalis is predicted
to suffer from a relatively high proportion of heterospecific matings. Although bees prefer M.
lewisii, they have been observed visiting M. cardinalis (Schemske and Bradshaw 1999). The
model predicts that when M. cardinalis is frequent, the preferred visits to M. lewisii will be
interspersed by visits to M. cardinalis resulting in heterospecific transfer of pollen.
During this experiment humming birds visited 138 plants but none of them were M.
lewisii indicating very strong preference. Unfortunately, using equation 1, preference is infinite
when no visits to the second species are observed. To overcome this problem I estimated the
proportion of visits to M. cardinalis to be exceedingly high (ψ = 0.996). Other studies have
documented hummingbirds visiting M. lewisii indicating this estimate is not unreasonable
(Schemske and Bradshaw 1999). Of note, the shapes of the curves in Figure 4 do not
qualitatively change when preference is increased ten-fold, indicating that if preference is very
strong the model is not sensitive to error in preference measurements.
DISCUSSION
My model predicts how reproductive isolation caused by pollinator behavior varies
across plant-pollinator communities. Specifically, I developed a quantitative framework for
understanding how the frequency of hybridizing plants and the frequency of pollinators affects
19
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pollinator mediated reproductive isolation in plants. This research focuses on two important
aspects of pollinator behavior – preference and constancy – that describe which plants a
pollinator visits and the order of plant visitation. Both aspects of behavior have been shown
empirically to contribute to plant speciation (Fenster et al. 2004; Kay and Sargent 2009), but this
is the first model that describes how variation in behavior leads to variation in the proportion of
heterospecific matings.
Model implications
My research is motivated by the observation that plant-pollinator communities vary over
geographic space and yet we lack a clear understanding of the implications of this variation for
plant reproductive isolation. As discussed below, other authors have addressed this problem in a
variety of ways. I took an analytical approach to derive the simplest model based on quantifiable
aspects of pollinator behavior, frequency of plant species, and frequency of pollinators in the
system to predict the proportion of heterospecific matings a plant will experience in a particular
community.
My model reveals some intuitive results – for example, reproductive isolation increases
as pollinator preference and constancy increase – as well as some non-intuitive results. I found
that the proportion of heterospecific matings (the inverse of reproductive isolation) decreases as
focal plant frequency increases in a community. The relationship between heterospecific matings
and plant frequency is non-linear and the shape of this curve is determined by the strength of
pollinator preference and constancy. I found that the stronger the behavior, the steeper the curve,
such that strong preference or constancy leads to low heterospecific matings even at low focal
plant frequencies.
20
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The relationship between plant frequency and proportion of heterospecific matings is
more complex in a multi-pollinator community. It has long been assumed, and observed, that if
two closely related plant species attract different pollinators that express opposing preferences,
than this specialization will result in reproductive isolation between the plants (Fenster et al.
2004; Kay and Sargent 2009). The advantage of pollinator specialization has been an emergent
property in other theoretical models describing plant-pollinator communities (Sargent and Otto
2006), but for the first time, I reveal how pollinator behavior causes this advantage. When
multiple pollinators have different preferences, their relative foraging efforts in a plant
community influence the predicted total proportion of heterospecific matings a focal plant
experiences. Yet, the pollinator with stronger preference has a disproportionately large influence
on the total proportion of heterospecific matings regardless of its frequency. In fact, the more
different two pollinators are in the strength of their preferences, the more total heterospecific
matings reflects the behavior of the pollinator with a stronger preference. This means that across
most plant and pollinator frequencies, a focal plant will experience a lower total proportion of
heterospecific matings if one pollinator prefers the focal plant and a second pollinator has
preference against the focal plant than if the second pollinator has no preference at all. In other
words, my model demonstrates that pollinator specialization is favored because pollinators with
different preferences interact non-additively to give the total proportion of heterospecific matings
a plant will experience.
Unlike with preference, constancy from two different pollinators does combine
additively to predict the total heterospecific matings. If two pollinators differ in the strength of
their constancy, then the total proportion of heterospecific matings predicted by these two
21
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pollinators is the average heterospecific matings predicted by each pollinator weighted by the
relative frequency of foraging visits made by each pollinator in the community.
Model applications
The results from my model provide expectations for how pollinator mediated
reproductive isolation should vary across populations that differ in plant and pollinator
composition. A strength of my model is that empirical observations of pollinator behavior in
natural or artificial plant communities can be used to predict pollinator mediated reproductive
isolation across a landscape. Specifically, pollinator preference can be calculated from
observations of proportion of visits a pollinator makes to multiple floral types and the proportion
of those floral types available. Pollinator constancy can be calculated from observations of the
pattern of movements pollinators make and the proportion of visits a pollinator makes to each
floral type. From these simple observations this model can predict reproductive isolation for any
pollinator frequency or plant frequency that occurs in nature. In Online Appendix C, I describe
specific examples of how this model can be applied using observations in Phlox and the
Mimulus. Because of the ease of applying this model to empirical data, my model can provide
novel insights into natural plant-pollinator communities. For example, it can explain why and
how hybridization and gene flow vary across natural plant hybrid zones. This model can also
make predictions about how hybridization will increase or decrease as climate change shifts
plant and pollinator ranges, phenology, and population sizes (Memmott et al. 2007).
The predictions from my model are based on simplifying assumptions including: 1.)
Pollinator preference and constancy are constant, 2.) The relevant spatial scale of plant
populations and pollinator foraging populations align, 3.) There are no spatially dependent
22
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aspects of pollinator foraging within the relevant scale of inquiry, 4.) Effectiveness of pollen
transfer is similar across pollinators, 5.) Plants are not pollinator limited such that heterospecific
matings are replaced with conspecific matings. It is likely that natural plant-pollinator
communities are more complicated than described by my model and violate some of these
assumptions. For example, some pollinators show frequency dependent preference (e.g.
(Cresswell and Galen 1991; Gigord et al. 2001; Smithson and Macnair 1996; Smithson and
MacNair 1997) and, as seen in Online Appendix A, this changes the predicted proportion of
heterospecific matings across populations. In other systems pollinators may vary their behavior
depending on the behavior and frequency of other pollinators in the community (e.g. (Brosi and
Briggs 2013; Fontaine et al. 2008; Inouye 1978)). The simplified model presented here can act as
a null against which variation in natural systems can be tested. In other words, if natural variation
in heterospecific matings does not conform to the expectations of the model, we now have a
powerful framework with which to test alternative hypotheses about what other factors affect the
proportion of heterospecific matings.
My model focuses specifically on the proportion of heterospecific matings and does not
consider total fitness of a plant. In other words, the model assumes that there are always enough
pollinators to pollinate flowers, and it is just a question of whether the delivered pollen is
conspecific or heterospecific. In many systems this assumption is violated (Ashman et al. 2004;
Burd 1994; Larson and Barrett 2000). I acknowledge that in a pollinator limited system the
proportion of heterospecific matings a plant experiences is not the only, or maybe even the most
important, source of selection. But, it is beyond the scope of this project to investigate how
frequency of plants and pollinators might affect total plant fitness if there is pollinator limitation
23
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and heterospecific matings. Extending the model to incorporate such scenarios is an important
future direction.
Previous theoretical research has considered aspects of plant-pollinator community
context to understand pollinator specialization, pollinator network structure (Bascompte et al.
2006), and how perturbations disrupt pollination (Kaiser-Bunbury et al. 2010; Memmott et al.
2004; Ramos-Jiliberto et al. 2012). Models such as these provide important insights into how and
why plant-pollinator communities might be structured as they are and how their current structure
can maintain biodiversity and stability. Some of these models have even incorporated explicit
aspects of pollinator behavior, such as adaptive foraging to reveal further insights (Valdovinos et
al. 2016; Valdovinos et al. 2013).
Conclusions
My model is unique in its reductionist view. My goal is to deconstruct the quantifiable
aspects of pollinator behavior to understand how variation in behavior contributes to
reproductive isolation across different plant communities. The model can generate predictions
about how temporal and spatial fluctuations in pollinator composition and plant composition
influences pollinator mediated reproductive isolation. This can be useful for empiricists to better
understand how the pollinator behavior they measure in the field leads to reproductive isolation
across changing communities. It is also useful for researchers studying plant speciation to
understand how components of reproductive isolation may vary across different populations.
Finally, this model is worthwhile at a theoretical level in that it brings together commonly used,
yet seemingly unrelated, equations for pollinator behavior and reproductive isolation to
analytically describe ethological isolation in plants.
24
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Online Appendix A: Generalized model for multiple pollinators and multiple plants
Equation 6 for total heterospecific matings generalized for n pollinators is
𝐻=
!!!
!!! 𝜐! 𝐻!
(A1)
where 𝐻! is the proportion of heterospecific matings predicted for pollinator i, and 𝜐! is the
proportion of total plants visits made by pollinator i. Note that
!!!
!!! 𝜐!
= 1.
The equation describing the heterospecific matings for each pollinator is
! !! (!!!)
!
𝐻! = !!! !!(!!!!
!! !! ! )
!
!
!
(A2)
! !
where 𝜅! and 𝜌! are constancy and preference of pollinator i for the focal plant.
Equation 7 for the total proportion of visits to a plant made by any pollinator i generalized for n
pollinators is
𝑣! =
!! !!
!!!
!!! !! !!
(A3)
where 𝜙! is the frequency of visits by pollinator i across all plants, such that the sum of all 𝜙!
across pollinators 1 through n equals 1. For each pollinator, 𝜓! is the proportion of visits it
makes to just the focal plant.
The total proportion of heterospecific matings for a give focal plant can be predicted from the
preference and constancy of each pollinators in a community with the following equation
𝐻=
!!!
!!!
!!
!"!
!!! !(!!!)
!"!
!!!
!!! !! !!! !(!!!)
∗
25
!! !! (!!!)
!!!! !!(!!!!! !!! !!! !! )
(A4)
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Online Appendix B: Model of frequency dependent pollinator behavior
Frequency dependent changes in pollinator preference affect the predicted proportion of visits by
a pollinator to the focal plant (ψ). The below equation describing proportion of visits by a
pollinator includes a frequency dependent parameter (b), which is the coefficient of frequencydependence as in Smithson and Macnair (1996):
𝜓=
!" !
!"
(B1)
! !(!!!)!
When b =1 there is no frequency dependent change in preference, when b>1 preference is
stronger for more frequent plants representing positive frequency-dependence, and when b<1
preference is less for frequent plants representing negative frequency-dependence.
The proportion of heterospecific matings a focal plant is predicted to experience for a single
pollinator i is
! !! (!!!)!
𝐻! = − (!!!)! !(!")!! !!(! !!!
!!
(B2)
!" ! )
The total heterospecific matings for a focal plant given n pollinators and frequency dependent
preference is
𝐻=
!!!
!!!
!
!"! !
!
!!! ! !(!!!)!!
!!
!"!
!!!
!!! !!
!!
!
!!!
!(!!!) !
!!
! !! (!!!)!!
∗ − (!!!)!! !(!")!! ! !!(! !!!
26
!! !
!" !! )
(B3)
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Online Appendix C: Using the model with empirical data
Phlox example with variation in constancy:
Pollinator observations of Battus philenor were performed on arrays of Phlox plants (Hopkins et
al. 2014). These arrays contained 10 light-blue P. drummondii plants, 10 dark-red P. drummondii
plants and 31 P. cuspidata plants. Both the number of flower types visited by the pollinators and
the number of transitions between each flower type was observed. I calculated proportion of
heterospecific matings separately for light-blue and dark-red P. drummondii and therefore
considered only the light-blue and P. cuspidata observations when calculating light-blue P.
drummondii proportion of heterospecific matings and only dark-red and P. cuspidata
observations when calculating dark-red P. drummondii heterospecific matings. Below I first
describe how to use the observed data to calculate the model parameters in order to predict
proportion of heterospecific matings for light-blue P. drummondii across all plant frequencies.
•
The frequency of focal plant (light-blue P. drummondii) is given.
f = 10/41=0.244
•
The total visits to light-blue P. drummondii (300) and P. cuspidata (172) are used to
calculate ψ (the proportion of visits to focal plant).
ψ = total visits to light-blue P. drummondii divided by total visits to both species
= 300/(300+172) = 0.635
•
Preference (ρ) is calculated from proportion of visits to focal plant (ψ) and frequency of
focal plant (f). This is a rearrangement of equation 1.
!!! !
𝜌 = !(!!!) = 5.41
27
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•
Proportion of heterospecific matings (H) observed is calculated from observed pollinator
transitions to light-blue P. drummondii from light-blue P. drummondii (73) and to lightblue P. drummondii from P. cuspidata (87).
Observed H = 73/(73+87) = 0.54
•
Constancy (k) is calculated using equation 2.
𝜅=
!!! !!
!!! !!!!!(!!!)
= -0.35
With preference (ρ) and constancy (𝜅), the model can be used to predict heterospecific mating
for any frequency of light-blue P. drummondii and P. cuspidata.
Now I describe how to use the observed data to calculate the model parameters to predict
proportion of heterospecific matings for dark-red P. drummondii across all plant frequencies.
•
The frequency of focal plant (dark-red P. drummondii) is given.
f = 10/41=0.244
•
The total visits to dark-red P. drummondii (266) and P. cuspidata (172) are used to
calculate ψ (the proportion of visits to focal plant).
ψ = total visits to light-blue P. drummondii divided by total visits to both species
= 266/(266+172) = 0.607
•
Preference (ρ) is calculated from proportion of visits to focal plant (ψ) and frequency of
focal plant (f). This is a rearrangement of equation 1.
!!! !
𝜌 = !(!!!) = 4.8
•
Proportion of heterospecific matings (H) observed is calculated from transitions to lightblue P. drummondii from light-blue P. drummondii (95) and to light-blue P. drummondii
from P. cuspidata (29).
28
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Observed H = 29/(29+95) = 0.23
•
Constancy (k) is calculated using equation 2.
𝜅=
!!! !!
!!! !!!!!(!!!)
= 0.36
With preference (ρ) and constancy (𝜅), the model can be used to predict heterospecific mating
for any frequency of dark-red P. drummondii and P. cuspidata.
Mimulus example with preference varying across two pollinators:
Pollinators were observed visiting mixed populations of Mimulus cardinalis and M. lewisii
(Ramsey et al. 2003). The identity of the pollinator (bee vs. hummingbird), the plant visited, and
the number of open flowers of each species were recorded. Two populations were observed but
most data came from one population so the proportion of open flowers from that population will
be used to calculated preference. The following data were observed:
•
On average there were 12.8 open M. lewisii flowers and 40.6 open M. cardinalis flowers,
which can be used to calculate the frequency of the focal plant (f).
fbee,cardinalis = 40.6/(12.8+40.6) = 0.76
fbee,lewisii = 12.8/(12.8+40.6) = 0.24
•
Bees visited 259 M. lewisii flowers and 3 M. cardinalis flowers, which can be used to
calculated proportion of visits to focal plant (ψ) from bee
ψbee,cardinalis = 3/262 = 0.011
ψbee,lewisii = 259/262 = 0.989
•
Bee preference (ρ) for the two flowers can be calculated from the frequency and
proportion of visits
𝜌!"",!"#$%&"'%( =
!!"#$%&"'%( !! !!"",!"#$%&"'%(
!(!!"",!"#$%&"'%( !!)
= 0.0035
29
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𝜌!"",!"#$%$$ =
•
!!"#$%$$ !! !!"",!"#$%$$
!(!!"",!"#$%$$ !!)
= 284.7
Hummingbirds visited 138 M. cardinalis flowers and no M. lewisii flowers. In order to
calculate proportion of visits and preference I used 0.5 as the number of M. lewisii flower
visits.
Ψbird,cardinalis = 138/138.5 = 0.996
Ψbird,lewisii = 0.5/138.5 = 0.004
𝜌!"#$,!"#$%&"'%( =
𝜌!"#$,!"#$%$$ =
•
!!"#$%&"'%( !! !!"#$,!"#$%&"'%(
!(!!"#$,!"#$%&"'%( !!)
!!"#$%$$ !! !!"#$,!"#$%$$
!(!!"#$,!"#$%$$ !!)
= 78.6
= 0.013
In total, hummingbirds visited 138 flowers and bees visited 262 flowers. From this I can
calculate ϕ, the proportion of visits to all plants made by each pollinator
ϕbee = 262/(138+262) = 0.655
ϕbird = 138/(138+262) = 0.345
With preference (ρ) for each pollinator and the frequency of visits by each pollinator in the
system (ϕ), the proportion of heterospecific matings for any M. cardinalis frequency can be
predicted using equation 8.
30
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